Subgroups — #23761476

Order 10112.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19098384	C₂	1	2	yes	maximal
2	C₄×C₁₆×C₇₉	C₂	1	1	yes	maximal, characteristic
3	#14579101	—	2	2	no	—
4	C₂×C₁₆×C₇₉	C₄	1	1	yes	characteristic
5	C₂×C₁₆×C₇₉	C₄	1	1	yes	characteristic
6	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
7	C₇₉⋊C₁₆	—	4	2	no	—
8	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
9	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
10	C₄²×C₇₉	Q₈	1	1	yes	characteristic
11	C₁₆×C₇₉	—	2	1	no	—
12	C₁₆×C₇₉	C₈	1	2	yes	—
13	C₂×C₄×C₇₉	—	2	1	no	—
14	C₂×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
15	C₈×C₇₉	C₂×C₈	1	1	yes	characteristic
16	C₈×C₇₉	M₁₆	1	1	yes	characteristic
17	C₈×C₇₉	D₈	1	1	yes	characteristic
18	C₈×C₇₉	Q₁₆	1	1	yes	characteristic
19	C₂²×C₇₉	#108	1	1	yes	characteristic
20	C₄×C₇₉	—	2	2	no	—
21	C₄×C₇₉	C₄⋊C₈	1	1	yes	characteristic
22	C₄×C₇₉	#107	1	1	yes	characteristic
23	C₂×C₇₉	—	2	1	no	—
24	C₂×C₇₉	#335	1	1	yes	characteristic
25	#1373	—	79	1	no	maximal, Sylow
26	C₇₉	#1373	1	1	yes	characteristic, complemented, Sylow
27	#364	—	79	2	no	—
28	C₄×C₁₆	D₇₉	1	1	yes	characteristic
29	M₃₂	—	158	2	no	—
30	C₂×C₁₆	Dic₇₉	1	1	yes	characteristic
31	C₂×C₁₆	Dic₇₉	1	1	yes	characteristic
32	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
33	C₂×C₈	D₃₁₆	1	1	yes	characteristic
34	C₂×C₈	C₂×Dic₇₉	1	1	yes	characteristic
35	C₄²	Dic₁₅₈	1	1	yes	characteristic
36	C₁₆	—	2	1	no	—
37	C₁₆	—	316	2	no	—
38	C₁₆	C₇₉⋊C₈	1	2	yes	—
39	C₂×C₄	—	2	1	no	—
40	C₂×C₄	C₄⋊Dic₇₉	1	1	yes	characteristic
41	C₈	C₂×C₇₉⋊C₈	1	1	yes	characteristic
42	C₈	#11929608	1	1	yes	characteristic
43	C₈	D₆₃₂	1	1	yes	characteristic
44	C₈	Dic₃₁₆	1	1	yes	characteristic
45	C₂²	#14579097	1	1	yes	characteristic
46	C₄	—	2	2	no	—
47	C₄	C₄⋊(C₇₉⋊C₈)	1	1	yes	characteristic
48	C₄	#14579095	1	1	yes	characteristic
49	C₂	—	2	1	no	—
50	C₂	#19098316	1	1	yes	characteristic

	subgroup	G/H
center	C₈	D₆₃₂
commutator	C₈×C₇₉	C₂×C₈
Frattini	C₄×C₈	C₂×D₇₉
Fitting	C₄×C₁₆×C₇₉	C₂
socle	C₂×C₇₉	#335
prime radical	C₂²×C₇₉	#108
cosocle	C₄×C₈×C₇₉	C₂²
hypercenter	C₄×C₁₆	D₇₉
hypocenter	C₇₉	#1373
LCS	G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
26. C₇₉	#1373	semidirect